Question

The mean of 100 observations is 49. By an error 60, 70, 80 are registered as 40, 20, 50 respectively. The correct mean is

• A. 48
• B. 52
• C. 54
• D. C

Answer 1

The Correct Option is D

Step 1: Compute the total sum of the original observations.

The mean of the 100 observations is given as 49. The total sum of the observations can be calculated as:

\[ \text{Total Sum} = \text{Mean} \times \text{Number of Observations} = 49 \times 100 = 4900. \]

Step 2: Identify the incorrect and correct values.

The incorrect values registered were \( 40, 20, 50 \), and the correct values should have been \( 60, 70, 80 \). The difference between the correct and incorrect values is:

\[ (60 - 40) + (70 - 20) + (80 - 50) = 20 + 50 + 30 = 100. \]

Step 3: Adjust the total sum to account for the correction.

The corrected total sum is:

\[ \text{Corrected Total Sum} = \text{Original Total Sum} + \text{Difference} = 4900 + 100 = 5000. \]

Step 4: Compute the corrected mean.

The corrected mean is:

\[ \text{Corrected Mean} = \frac{\text{Corrected Total Sum}}{\text{Number of Observations}} = \frac{5000}{100} = 50. \]

Final Answer: The corrected mean is \( \mathbf{50} \), which corresponds to option \( \mathbf{(4)} \).